Let U be the set of all possible 5-letter words made from copies of X, Y, and Z. What is the cardinality of U? Let S₁ be the set of words in U where the first and second letters are identical. Let S2 be the set of words where the second and third letters are identical. Define S3 aimilonker What alition of S ♡ C 182

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Consider the 5-letter words that are made from copies of X, Y, and Z. We want to use
inclusion-exclusion to count the number of such words that do not have any repeated
consecutive letters. Thus we want to count words such as YXZXY, but not ZYXXZ.
(i) Let U be the set of all possible 5-letter words made from copies of X, Y, and Z.
What is the cardinality of U?
(ii) Let S₁ be the set of words in U where the first and second letters are identical. Let
S2 be the set of words where the second and third letters are identical. Define S3
and S4 similarly. What are the cardinalities of S1, S2, S3, and S4?
Transcribed Image Text:Consider the 5-letter words that are made from copies of X, Y, and Z. We want to use inclusion-exclusion to count the number of such words that do not have any repeated consecutive letters. Thus we want to count words such as YXZXY, but not ZYXXZ. (i) Let U be the set of all possible 5-letter words made from copies of X, Y, and Z. What is the cardinality of U? (ii) Let S₁ be the set of words in U where the first and second letters are identical. Let S2 be the set of words where the second and third letters are identical. Define S3 and S4 similarly. What are the cardinalities of S1, S2, S3, and S4?
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